The invention relates to active acoustic attenuation systems, and provides a system for cancelling undesirable output sound in a duct for higher order mode non-uniform sound fields. The invention arose during continuing development efforts relating to the subject matter shown and described in U.S. Pat. Nos. 4,677,677, 4,677,676 and 4,665,549, and allowed U.S. application Ser. No. 922,282, now U.S. Pat. No. 4,736,431 filed Oct. 23, 1986, all assigned to the assignee of the present invention and incorporated herein by reference.
A sound wave propagating axially through a rectangular duct has a cut-off frequency f.sub.c =c/2L where c is the speed of sound in the duct and L is the longer of the transverse dimensions of the duct. Acoustic frequencies below the cut-off frequency f.sub.c provide plane and uniform pressure acoustic waves extending transversely across the duct at a given instant in time. Acoustic frequencies above f.sub.c allow non-uniform pressure acoustic waves in the duct due to higher order modes.
For example, an air conditioning duct may have transverse dimensions of two feet by six feet. The longer transverse dimension is six feet. The speed of sound in air is 1,130 feet per second. Substituting these quantities into the above equation yields a cut-off frequency f.sub.c of 94 Hertz.
In circular ducts similar considerations apply when the duct diameter is approximately equal to one-half of the wavelength. Exact equations may be found in L. J. Eriksson, Journal of Acoustic Society of America, 68(2), Aug. 1980, pp. 545-550.
Active attenuation involves injecting a cancelling acoustic wave to destructively interfere with and cancel an input acoustic wave. In the given example, the acoustic wave can be presumed as a plane uniform pressure wave extending transversely across the duct at a given instant in time only at frequencies less than 94 Hertz. At frequencies less than 94 Hertz, there is less than a half wavelength across the longer transverse dimension of the duct. At frequencies above 94 Hertz, the wavelength becomes shorter and there is more than a half wavelength across the duct, i.e. a higher order mode with a non-uniform sound field may propagate through the duct.
In an active acoustic attenuation system, the output acoustic wave is sensed with an error microphone which supplies an error signal to a control model which in turn supplies a correction signal to a cancelling loudspeaker which injects an acoustic wave to destructively interfere with the input acoustic wave and cancel same such that the output sound at the error microphone is zero. If the sound wave traveling through the duct is a plane wave having uniform pressure across the duct, then it does not matter where the cancelling speaker and error microphone are placed along the cross section of the duct. In the above example for a two foot by six foot duct, if a plane wave with uniform pressure is desired, the acoustic frequency must be below 94 Hertz. If it is desired to attenuate higher frequencies using plane uniform pressure waves, then the duct must be split into separate ducts of smaller cross section or the duct must be partitioned into separate chambers to reduce the longer transverse dimension L to less than c/2f at the frequency f that is to be attenuated.
In the above example, splitting the duct into two separate ducts with a central partition would yield a pair of ducts each having transverse dimensions of two feet by three feet. Each duct would have a cut-off frequency f.sub.c of 188 Hertz.
The above noted approach to increasing the cut-off frequency f.sub.c is not economically practicable because active acoustic attenuation systems are often retrofitted to existing ductwork, and it is not economically feasible to replace an entire duct with separate smaller ducts or to insert partitions extending through the duct to provide separate ducts or chambers.
The present invention solves the above noted problem in a particularly simple and cost effective manner. The invention provides a method for increasing the frequency range of an active acoustic attenuation system in a duct without increasing cut-off frequency f.sub.c of the duct or otherwise splitting the duct into separate ducts or partitioning the duct into separate chambers.
The invention eliminates the need to reduce the longer transverse dimension L of the duct to less than c/2f. Instead, the invention increases the frequency range above f.sub.c to include higher order modes. A plurality N of cancelling model sets are provided. Each set has its own adaptive filter model, cancelling speaker, and error microphone. A single input microphone may service all sets. The duct has a transverse dimension greater than a half wavelength, and there is non-uniform acoustic pressure transversely across the duct at a given instant in time.
The invention can also be used with modes that have non-uniform pressure distribution in both transverse dimensions of a rectangular or other shape duct. The invention may also be used with modes that have non-uniform pressure distribution in both the radial and circumferential dimensions of a circular duct.
In general, the invention provides an active attenuation system for attenuating an undesired elastic wave in an elastic medium. The elastic wave propagates axially and has non-uniform pressure distribution transversely across the medium such that the wave has a plurality of portions in the transverse direction at a given instant in time, including at least one positive pressure portion and at least one negative pressure portion. A plurality of output transducers are provided, one for each of the positive and negative pressure portions of the undesired elastic wave. The output transducers introduce a plurality of cancelling elastic waves into the medium. A plurality of error transducers are provided, one for each of the positive and negative pressure portions of the undesired elastic wave. The error transducers sense the combined undesired elastic wave and the cancelling elastic waves, and provide a plurality of error signals. A plurality of adaptive filter models are provided, one for each of the positive and negative pressure portions of the undesired elastic wave. Each model has an error input from a respective error transducer, and outputs a correction signal to a respective output transducer to introduce the respective cancelling elastic wave. Each of the positive and negative portions of the undesired elastic wave has its own set of an adaptive filter model, output transducer, and error transducer.